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Basic Algebra
Solving Multiple Equations By Graphing: At a Glance

Introduction to Solving Multiple Equations By Graphing:

Occasionally you will be given two linear equations and asked to solve for x and y. There are numerous ways to do this, including graphing the lines, substitution, and elimination. However, in pre-algebra we will only touch on the first: solving by graphing.

Solve for x AND y:

y = 2x - 2

y = -3/2x + 5

What this question is really asking: find the (x,y) point where these lines meet.

How to Solve Systems of Equations by Graphing

Graph both lines on the same coordinate grid. Since they are both in slope-intercept form, we can do this by plotting the intercepts then using the slope to find another point.

graph

It is pretty clear where these lines meet, at the point (2, 2), which is our answer!

Look Out: be sure to write your answer as a point in (x, y) form.

Solving Multiple Equations By Graphing Practice:

Example 1

Solve this system of equations for x and y:

y = -8

y = -4x + 4


Example 2

Solve this system of equations for x and y:

y = 1/2x + 2

-3x + y = 2


Example 3

Solve this system of equations:

x = 5

y = -1


Exercise 1

Solve this system of equations by graphing:

y = -x + 1

x = 1/3x - 3


Exercise 2

Solve this system of equations by graphing:

y = 4

y = 2x + 1


Exercise 3

Solve this system of equations by graphing:

-3x + y = 6

x + 2y = -2


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